1. EE 372 Fundamentals of Power Systems
Textbook:
John J. Grainger, William D. Stevenson, Jr., “Power System Analysis”, McGraw-Hill, Inc., 1994.
Objective: To teach the fundamental concepts of electric power system engineering.

2. Basics Power: Instantaneous consumption of energy Power Units
Watts = voltage x current for dc (W)
kW – 1 x 103 Watt
MW – 1 x 106 Watt
GW – 1 x 109 Watt

3. Basics Energy: Amount of Work Energy Units (for electrical power)
Wh x 100 Watthour
kWh – 1 x 103 Watthour
MWh – 1 x 106 Watthour
GWh – 1 x 109 Watthour
Relationship of power and energy
Energy Consumed
Average Power
Duration

4. Sinusoidal Signals
Circular rotation of a magnetized rotor in Synchronous Generator
produces sinusoidal voltage in stator windings due to FARADAY LAW.
(Look at EE 471 Notes)

5. Sinusoidal Signals
THREE-PHASE SYNCHRONOUS GENERATOR

6. ? ? Sinusoidal Signals How do you write the mathematical
equation for this periodic function? ? ?

7. Sinusoidal Signals
Period : 0.01 s.
Frequency : 100 Hz.

8. Sinusoidal Signals
Period : 0.02 s.
Frequency : 50 Hz. OR

9. Sinusoidal Signals

10. ? Sinusoidal Signals Peak voltage : 310 V. Period : 0.02 s.
-400
-300
-200
-100
100
200
300
400
0.0000
0.0025
0.0050
0.0075
0.0100
0.0125
0.0150
0.0175
0.0200
Time (seconds)
Volts, Amperes
Current
Voltage
Peak voltage : 310 V.
Period : s.
Frequency : 50 Hz.
radian
Peak current : 150 A.
Period : s.
Frequency : 50 Hz.

11. Complex Numbers
Euler’s Formula : Relates exponential and sinusoidal functions Re Im
Rectangular
Notation
Polar R
Attention:

12. Complex Numbers Rectangular Polar
Addition and subtraction of complex numbers are easier with
the rectangular notation.
Multiplication and division of complex numbers are easier with
the polar notation.
Attention:
Rectangular
Polar

13. Phasors Phasors are complex numbers used to represent sinusoids.
Phasor representation of a sinusoidal function:
Phasor
If we multiply phasor by
and apply Euler’s formula

14. Phasors
Consider the derivative of sinusoidal signal represented as a phasor
Derivative:

15. Phasors
Examples:
Inductor
Capacitor

16. Phasors
Ref.
Important: In power systems, RMS values are used for the magnitudes.

17. Phasors
v(t)
i(t)